Which is not the property of the transformation rotation

From the given transformation which pre image is not equal to image

Transformation is a mechanism that transform an object into different structures.
In General, there are 4 types of transformations. They are;
1. Reflection
2. Rotation
3 Translation
4. Dilation.
Except Dilation, all the transformation techniques are termed as rigid transformations since, they provide same structure as the object.

From the given transformation which is not a rigid transformation

* Transformation is the mechanism that changes one image to other by performing the below techniques.
* Reflection, Rotation, Dilation, Translation.
* Since, In Reflection, Rotation, Dilation the size and shape of the object remains constant. They were called as Rigid Transformation.
* In Dilation, the object's structure got changed and hence, it is termed as a non- rigid Transformation.

Pick the odd one out

Hence, we can say that only one option that Rotation is a transformation which slides across the plane is wrong because the rotation transition always slide across a point.

In the transformation rotation at what degree measure image match with its pre image.

Given Data:
                  In the transformation rotation at what degree measure image match with its pre image.
>>>We were asked to find the Angle of Rotation that rotates to exactly to it's point.
>>>Hence, let the point in the space be (x, y) then it's rotation should be (x, y).
>>>Finely, The rotated coordinates are in the form:
(x', y') =  
>>>From the given data:
(x', y') = (x, y)
* By comparing the above Equation's we get:
x = (x cos - y sin) and y = y cos + x sin
>>>By solving the above Equation's we get:
          (x  y) =  (x  y) cos - y² sin
and    (x  y) =   (x  y) cos + x²sin
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0 =(x²+y²)sin
-->sin=0
-->    =360 degrees.
>>>Hence, the Angle of Rotation is 360 degrees.

In the transformation rotation occurs with respect to

Rotation means the Circular movement of an object around one fixed point.
* Hence, it is called as a rigid transformation.
* Hence, we can say that the rotation meant that the rotation of an object about a fixed point.

In which rotation movement does (x, y)      (-x, -y)

Given Data:
In which rotation movement does (x, y)      (-x, -y)
***we were asked to find the Angle of Rotation of a point (x, y) to rotate it to (-x, -y).
>>>The rotated coordinates are:
(x', y') =  (x cos - y sin , y cos + x sin)
>>>From the data given  (x', y') = (-x, -y)
* Hence, By comparing the above equation's we get:
               -x = x cos - y sin and  -y = y cos + x sin. Then
* By solving the above equation's we get:
              (y - x) = (y  x ) cos - y² sin
              (-y  x) = (y  x ) cos + x²sin
            ___________________________________
                       0   = 0 + (x²+y²)sin

sin=0
 = 180 degrees or -180 degrees.
***Hence, the Angle of Rotation to rotate the point (x, y) to (-x, -y) is counter clockwise 180 degrees and clockwise 180 degrees.

In which rotation movement does (x, y)      (-y, x)

Given Data:
In which rotation movement does (x, y)      (-y, x)
>>>We were asked to find the angle of rotation of a point to rotate a point from (x, y) to (-y, x).
*** Rotated coordinates are:
(x', y') =  (x cos - y sin , y cos + x sin)
>>Here, the rotated points are :
              (x', y') = (-y, x).
* Hence, By comparing the above equation's we get:
             -y =  x cos - y sin ; and x = y cos + x sin
Hence, By solving the above equation's we get:

            (x  -y) = x²cos - (x  y)sin
and      (y  x) = y² cos + (x  y)sin
          ________________________________
                      0 = ( x² + y²)cos 

* Hence, cos =0 leads to 90 degrees or -270 degrees.
>>>>Therefore, the Angle of Rotation is counter clockwise 90 degrees and clockwise 270 degrees.

In rotation of clockwise movement maps (x , y) (y,-x)

Given Data:
The point (x, y) is transformed to (x , y) (y,-x) in clockwise direction.
>>> we were asked to find the Angle of Rotation.
>>>The coordinates of a point (x, y) after rotation through 90 degrees in clockwise direction are:
(x', y') = (x cos - y sin , y cos + x sin)
>>>we were given that (x', y') = (y, -x)
>>> (y, -x) = (x cos - y sin , y cos + x sin)
    Hence, y = x cos - y sin and -x = y cos + x sin
By solving the above equation's we get:
              (x  y)  = x²cos - (x  y) sin
and        (y  -x) = y²cos + (x  y) sin

__________________________________
0 = (x²+y²)cos
*This implies cos=0, then:
 = 90 degrees.
>>>Therefore, the angle of rotation is 90 degrees.

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